Controlling chaos and Neimark-Sacker bifurcation in a discrete-time predator-prey system

Abstract

This article is about a discrete-time predator-prey model obtained by the forward Euler method. The stability of the fixed point of the model and the existence conditions of the Neimark-Sacker bifurcation are investigated. In addition, the direction of the Neimark-Sacker bifurcation is given. Moreover, OGY control method is to implement to control chaos caused by the Neimark-Sacker bifurcation. Finally, Neimark-Sacker bifurcation, chaos control strategy, and asymptotic stability of the only positive fixed point are verified with the help of numerical simulations. The existence of chaotic behavior in the model is confirmed by computing of the maximum Lyapunov exponents.

Stability Analysis of a Discrete Time Prey-Predator Population Model with Immigration

“…We have seen that there is no chance of Neimark-Sacker bifurcation to occur in the system (4). We present the Flip bifurcation diagrams and Maximum Lyapunov exponent for the system (4) by choosing bifurcation parameter as immigration instead of the step size .Also, to control the chaos in the system (4), we study the OGY Feedback control method [24]. Numerical simulations are presented to support obtained theoretical results and to show the complex dynamical behaviors.…”

Mathematical Analysis of Discrete Fractional Prey-Predator Model with Fear Effect and Square Root Functional Response

“…Based on observed ecological interactions among individuals of the species at various trophic levels, mathematical modelling is a helpful tool for understanding and predicting the long-term survival of various species. There are different types of preypredator models, such as the continuous model [1][2], discrete model [3][4][5], fractional model [6][7][8][9], etc. Nowadays, the fractional-order system can explain more natural phenomena that were previously ignored by the classical theory of the integer-order dynamical system.…”

A New Convex Controller for Stabilizing of Two Symmetrical Logistic Maps

“…It is proved to possess a variety of regular and chaotic attractors with a complex geometry of the basins of attraction. It also has closed invariant curves along with equilibrium and discrete cycles as an output of Neimark-Sacker bifurcation [15] and Hopf bifurcation [16][17][18]. The present work aims to study the coupled logistic map's attractors (equilibrium, closed invariant curves).…”